7.1 BMI Boxplots of Athletes’ Height, Weight and Age

The above chart comparing height against categories show averages between female and male athletes are not equal across the board. It does not matter if the Olympian is underweight or obese, the male athletes are on average taller than the female athletes. For healthy and overweight athletes, there are more outliers in the data than the underweight and obese categories. This chart shows that average weight increases from underweight to obese. This is what we would expect. There is very little variability in weight for underweight Olympians and much greater variablity in the weight for obese athletes. As we found with height, the male athletes on average weigh more than the female athletes.

Average ages are close irrespective of weight category or gender. Notable are the number of outliers in age data for healthy and overweight Olympians.

7.2 Boxplot of All Olympic Athletes BMI

The histogram of relative frequency versus BMI of female and male Olympians clearly show that not all athletes have healthy weight according to the CDC.

7.3 Boxplot of BMI vs Sport (Summer)

We wondered about the differences between Olympians who competed in summer versus winter events.

In the summer events, the boxplots show that athletes in the overweight category competed in basketball, boxing, football, ice hockey, rugby, shooting, tug-of-war, weightlifting, and wrestling. There was great variability in BMI for weightlifters, at the top – they were considered obese. In In the underweight category were female rhythmic gymnasts and gymnasts.

7.4 Boxplot of BMI vs Sport (Winter)

In the winter events, the boxplots showed male athletes in the overweight category competed in alpine sking, bobsleigh, curling, freestyle skiing, ice hockey, luge, and snowboarding. The female figure skaters were in the underweight category. Given that there are not that many events in the winter Olympics but athletes in half of the events are upper end of healthy weight to being overweight, it seems that more Winter Olympians are in the upper end of normal to being overweight. The nature of winter events requiring athletes to be bulkier and bigger in order to be competitive.

7.5 Boxplot of BMI vs Top 10 Events

The boxplot showing BMI data for top 10 events with the most athletes is easier to read and confirms that for events such as basketball, handball, ice hockey, water polo, and wrestling the male athletes are considered overweight by CDC standards. The lower end of the weight categorization is gymnastics.

7.6 BMI of Medal Winning Athletes

We looked at sporting events in order to learn about summer versus winter athletes and found there are more overweight winter athletes. The events played a strong role in determing the BMI classification of the athletes. We wanted to find out winning a medal also show common characeristics between athletes. Did Gold/Silver/Bronze medalists have more in common with each other irrespective of events they competed in?

The boxplot and histograms showing BMI data for Gold/Silver/Bronze medal winners was relatively normal.

We created a scatterplot of height and weight of athletes that competed in the top 10 events to discern groupings based on event but did not find any conclusive visual evidence.

7.7 US Olympic Team

We haveve looked at data from the perspective of season, events and medals. Let’s focus on US Olympic Team data in table format to see if we can draw any conclusions.

Gymnasts on the US Olympic team are on the lower spectrum of healthy weight range. Wrestlers were second shortest but they have the highest BMI, making them classified as overweight. Consistent with the analysis we found in previous sections, US wrestlers and ice hockey players were classified as overweight.

7.8 T-Intervals 95% confidence

7.9 T-Test

The p-value 2.2e-16 being small enough to be considered 0, hence used a two-sided test we can reject the null hypothesis that the means of BMI values being equal between male and female Olympians The plots indicate that male Olympian athletes’ BMI to be greater than female Olympian athletes. Female and male athletes BMI: 21.9, 24.0

7.10 Anova Test comparing BMI Averages of Athletes From Different Olympic Sporting Events

               Df Sum Sq Mean Sq F value              Pr(>F)    
Sport          14  16916    1208     205 <0.0000000000000002 ***
Residuals   18632 109780       6                                
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

The small p-value would confirm that there are significant differences in BMI averages of athletes in each sports which can be confirmed by the plots from sections 4.3-4.4

Many Olympic athletes’ builds are more muscular than the average person. They may have BMI that are technically categorized as overweight but it is not necessarily unhealthy. Many BMI charts point out it improperly categorizes athletes and our analysis confirms this.

8.1 Additional Datasets

The Olympics dataset obtained previously is merged with datasets containing the Gross Domestic Product (GDP) and population of each country for the years 1960-2019. The datasources were:

Population:

https://knoema.com/UNWPP2019/world-population-prospects-2019

(obtained from worldbank.org)

GDP:

https://data.worldbank.org/indicator/NY.GDP.MKTP.CD

Both datasets had missing data for several of the past decades and for some of the countries that did not participate in the Olympics. Also, for the recent years some of the countries that did participate still had missing data. These were filled by extrapolating the average of the years the preceded/followed the missing data. Furthermore, gross domestic product per capita (GDPpC) was calculated by dividing the GDP over the population. Categorical variables of the data are converted into ‘factor’ class.

8.2 EDA

As a first step to the EDA, for the year 2000 until present, bar charts of the total number of medals won by each country and gross domestic product per capita (GDPpC) were plotted for preliminary comparison.

Looking at a few randomly picked countries the following is obsereved:

The table does not directly show a clear and distinct relationship between countries winning medals and their GDP/population. Scatter plots, histograms and pair plots (pairs.panels show bivariate scatter plots below the diagonal, histograms on the diagonal, and the Pearson correlation above the diagonal) are shown below to further investigate the relationship. To simplify the plots, the average GDP, population and GDP per capita are calculated for years of 2000 until present. Also, the outliers were identified using “boxplot.stats” and a plots are split into “with outliers” and “without outliers” are made.

8.3 Relationship between Medals Won and Competing Country’s GDP per Capita (year 2000-present)

The scatter plots show a positive uptrend. Also the pairplots show a stronger correlation between average GPD and number of medals won when compared to population and GDPpC. The table below summarizes the numbers

8.4 Relationship Between Sports and Competing Country’s GDP per Capita (year 2000-present)

Another relationship to explore is the number of medals won in a particular sport and the GDP, population and GDPpC of the competing countries.The plots below show scatter and pair plots for three sports. Each exhibiting a different relationship to population, GDP and GDPpC.

The results showed that each sport has a different relationship with when compared with the relevant countries GDPpC. Where swimming has a positive uptrend with GDPpC, boxing is neutral and canoeing has a negative downtrend. The table below summarize the calculated correlation factor for three sports.

The Residuals vs Leverage plots below show that none of the datapoints are highly influential against a regression line.

8.5 Additional Information

The results of this investigation could be further improved if the data on the percentage of the GDP that gets allocated to the Olympic Committee of each of these countries. Also, the world happiness report, Corruption Perceptions Index, life expectancy and literacy index could all be included to develop a well rounded look into the various factors that my affect an athlete’s performance due to the environment they lived in.

9.1 Trends in Specific Sports

We wanted to see the changes in Olympians for the top 10 events (in terms of how many Olympians were recorded for the sport) over the years. Below are the top 10 events:

It seems that in general events like rowing or basketball have been trending towards larger and larger athletes (in terms of both weight and height) whereas events like Gymnastics skews in the completely opposite direction, favoring smaller and smaller athletes. The Wrestling event data is a bit misleading—we have taken the averages per Olympic game year, and if we were to look at the Wrestling data by itself we would see clear categories for weight and height. This is due to the nature of the sport, and its weight classes. This is why in the men’s data it looks like the data for the Wrestling is a constant straight line. It appears that way because there the following weight classes at the Olympics: Freestyle weight classes (12): Men’s 57kg, Men’s 65kg, Men’s 74kg, Men’s 86kg, Men’s 97kg, Men’s 125kg, Women’s 50kg, Women’s 53kg, Women’s 57kg, Women’s 62kg, Women’s 68kg, Women’s 76kg; and then Greco-Roman weight classes (6): Men’s 60kg, Men’s 67kg, Men’s 77kg, Men’s 87kg, Men’s 97kg, Men’s 130kg.

9.2 Changes in Weights and Heights Over The Decades

What we can also use this over time data for is to see trends during “decades”. We can overlay the data for the decades ontop of each other on a histogram, or we could use boxplots where we’ve made a decade into a “rank”/factorial data type.

Now that we’ve created a new comlumn Decade in the dataframe, we can make histograms or boxplots of the Weight and Height and group by Decade.

9.3 ANOVA Testing on the Trends Over the Decades

We have the boxplots, but we can use ANOVA to test the difference between the means in the weight and height data over the decades. ANOVA testing we have that:

1. Null hypothesis: the means of the different groups are the same
2. Alternative hypothesis: At least one sample mean is not equal to the others.

In one-way ANOVA test, a significant \(p\)-value indicates that some of the group means are different, but we don’t know which pairs of groups are different. We use a significance level of \(\alpha = 0.05\).

Here is the ANOVA test for the weight data over the decades

               Df  Sum Sq Mean Sq F value Pr(>F)  
Decade         12    4547     379    1.68  0.063 .
Residuals   30168 6790473     225                 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

We can see that for aov(Weight ~ Decade, data=athlete_events_noNA), we have \(p\) = 6.341e-02. The \(p\)-value here is not significant, which means that over time, the mean weight of the athletes is not significantly different between the decades.

Here is the ANOVA test for the height data over the decades

               Df  Sum Sq Mean Sq F value           Pr(>F)    
Decade         12   10066     839    7.05 0.00000000000058 ***
Residuals   30168 3591551     119                             
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

We can see that for aov(Height ~ Decade, data=athlete_events_noNA), we have \(p\) = 5.807e-13. The \(p\)-value here is very significant, which means that over time, the mean height of the athletes is significantly different between the decades.

9.4 Summary of changes over time in weights and heights of olympic athletes

To see the changes in the athletes’ weights and heights over time we narrowed our analysis to just the “top 10” events. A “top” event was simply defined by the total number of athletes that had participated in said event in total, which meant that although we were reducing the number of data analyzed we still had a large amount of athletes still left to look at. The category “Athletics”, although the most “popular” in terms of it being the event with the single highest number of participants, was excluded due to the remarkable diversity of subcategories included in that one single event (which includes track and field, road running, cross country running, and race walking). This diversity of subcategories made it difficult to determine how the average athlete in said event looks, unlike the other events which are single sports such as basketball or swimming.

It seems that over time the weights and heights of Olympic athletes has been moving towards extremes. We can see how, for example, the Olympians in gymnastics have become much lighter and much shorter, while the opposite is true for events like basketball, rowing, and swimming. We see that being an Olympic athlete very much means that your body type is an outlier, and the kind of outlier it is (very light or heavy, very short or tall) is influenced by the type of event that the athlete is competing in. We can see just how the number of outliers in the weights and heights of the athletes increases as we go through the decades, where the most recent decade of Olympic games shows the most outliers in both weight and height data than any other decade.

10.1 Plots

It appears that the mean age that an Olympic Medalist wins a medal is around 26 years old. We can also look at the ages of medal-winning athletes separated by the Summer and Winter Games.

From the plots we can see that between WW1 and WW2 the average age of medalists is decreasing, but after WW2 the average age temporarily rose. We see that the age begins to decrease until 1980 but then rises again after 1980. The age seems to plateau in the 2010s.

It seems that there are fewer peaks and dips in the Winter Games data than in the Summer Games data, where the Winter Athletes seem to have a smaller variance in age. We can look at the Summer and Winter Games together.

It appears that after the 1950s the athletes at the Winter Games, on average, are older. Both Summer and Winter Games experience an upward trend in ages after the 1980s.

We can also look at the breakdown of ages between Season and Gender.

When we look at the medal-winning athletes during the Summer Games by gender we see that in general men get medals at older ages than women do. Just as with the Summer Games we see that, on average, male athletes tend to be older than female athletes.

10.2 Summary of changes over time in ages of olympic athletes

While the weights and heights of the athletes seem to be affected by the event in which they particpate (or, rather, that athletes with extreme body types perhaps go to the Olympics more than individuals with “average” body types), the ages of the Olympic athletes seems to be affected by global events—which makes sense, considering that the Olympics are, in and of themselves, global events. The overall average age of all Olympians, even amongst the medals winners, is roughly 26 years old.

During the two World Wars the average ages of the athletes are higher than other periods, presumably because the younger athletes we fighting in the wars. A good three quarters of the Olympic athletes have been men, and so it makes sense to see this shift in the mean age when we suddenly lose a good majority of the young male athletes to war. After WW2 we see a decrease in the average age of Olympians, indicating that we have a new group of young atheletes participating in the games. Since roughly the 1980s, there has been a slow increase in the average ages of Olympians. On average female athletes have fairly consistently been younger than their male counterparts, and the Olympians participating in the Winter games are younger than the Olympians participating in the Summer games.